Modeling Stand Density Effects on Taper for Jack Pine and Black Spruce Plantations Using Dimensional Analysis

Abstract

A taper equation was developed for jack pine and black spruce trees growing at varying density using a dimensional analysis approach. Data used in this study came from stem analysis on 1,135 jack pine (Pinus banksiana Lamb.) and 1,189 black spruce (Picea mariana [Mill.] B.S.P.) trees sampled from 25 even-aged monospecific plantations in the Canadian boreal forest region of Northern Ontario. About half of the trees were randomly selected for model development, with the remainder used for model evaluation. A nonlinear mixed-effects approach was applied in fitting the taper equation. The predictive accuracy of the model was improved by including random-effects parameters for a new tree based on upper stem diameter measurements. Three scenarios of using upper stem diameter measurements to predict random effects were examined for predictive accuracy: one diameter at any height along the bole; two diameters, one each from below and above breast height; and three diameters, one from below and the other two from above breast height. The upper height at which the diameter was measured was limited to 65% of total tree height for practical reasons. For the first scenario, the model calibrated using a diameter measurement from between 34 and 38% of total height provided the best predictions of inside-bark diameters. For the second scenario, the model calibrated using one diameter from near the stump and the other from close to 65% of total height produced the least bias in predicting inside-bark diameters. For the third scenario, the model calibrated using the diameters from near the stump and at approximately 35 and 65% of total height provided the highest prediction accuracy.

Picea mariana, Pinus banksiana, tree form, stem profile models, stand density, thinning, nonlinear regression, fixed response, calibrated response, mixed-effects model